btj \dZddlmZddlmZddlZddlmZddgZ d d Z d d Z d d Z d Z dS)zB Cuthill-McKee ordering of graph nodes to produce sparse matrices )deque) itemgetterN)arbitrary_elementcuthill_mckee_orderingreverse_cuthill_mckee_orderingc#Ktj|D]+}t|||Ed{V,dS)aGenerate an ordering (permutation) of the graph nodes to make a sparse matrix. Uses the Cuthill-McKee heuristic (based on breadth-first search) [1]_. Parameters ---------- G : graph A NetworkX graph heuristic : function, optional Function to choose starting node for RCM algorithm. If None a node from a pseudo-peripheral pair is used. A user-defined function can be supplied that takes a graph object and returns a single node. Returns ------- nodes : generator Generator of nodes in Cuthill-McKee ordering. Examples -------- >>> from networkx.utils import cuthill_mckee_ordering >>> G = nx.path_graph(4) >>> rcm = list(cuthill_mckee_ordering(G)) >>> A = nx.adjacency_matrix(G, nodelist=rcm) Smallest degree node as heuristic function: >>> def smallest_degree(G): ... return min(G, key=G.degree) >>> rcm = list(cuthill_mckee_ordering(G, heuristic=smallest_degree)) See Also -------- reverse_cuthill_mckee_ordering Notes ----- The optimal solution the bandwidth reduction is NP-complete [2]_. References ---------- .. [1] E. Cuthill and J. McKee. Reducing the bandwidth of sparse symmetric matrices, In Proc. 24th Nat. Conf. ACM, pages 157-172, 1969. http://doi.acm.org/10.1145/800195.805928 .. [2] Steven S. Skiena. 1997. The Algorithm Design Manual. Springer-Verlag New York, Inc., New York, NY, USA. N)nxconnected_components connected_cuthill_mckee_orderingsubgraph)G heuristiccs P/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/networkx/utils/rcm.pyrrs`j $Q ' 'NN3AJJqMM9MMMMMMMMMMNNcXttt||S)aGenerate an ordering (permutation) of the graph nodes to make a sparse matrix. Uses the reverse Cuthill-McKee heuristic (based on breadth-first search) [1]_. Parameters ---------- G : graph A NetworkX graph heuristic : function, optional Function to choose starting node for RCM algorithm. If None a node from a pseudo-peripheral pair is used. A user-defined function can be supplied that takes a graph object and returns a single node. Returns ------- nodes : generator Generator of nodes in reverse Cuthill-McKee ordering. Examples -------- >>> from networkx.utils import reverse_cuthill_mckee_ordering >>> G = nx.path_graph(4) >>> rcm = list(reverse_cuthill_mckee_ordering(G)) >>> A = nx.adjacency_matrix(G, nodelist=rcm) Smallest degree node as heuristic function: >>> def smallest_degree(G): ... return min(G, key=G.degree) >>> rcm = list(reverse_cuthill_mckee_ordering(G, heuristic=smallest_degree)) See Also -------- cuthill_mckee_ordering Notes ----- The optimal solution the bandwidth reduction is NP-complete [2]_. References ---------- .. [1] E. Cuthill and J. McKee. Reducing the bandwidth of sparse symmetric matrices, In Proc. 24th Nat. Conf. ACM, pages 157-72, 1969. http://doi.acm.org/10.1145/800195.805928 .. [2] Steven S. Skiena. 1997. The Algorithm Design Manual. Springer-Verlag New York, Inc., New York, NY, USA. )r)reversedlistr)rrs rrrHs)j D/YGGGHH I IIrc#K|t|}n ||}|h}t|g}|r|}|Vt|t |||z t d}d|D}|||||dSdS)Nkeycg|]\}}|Sr).0nds r z4connected_cuthill_mckee_ordering..s%%%$!QA%%%r) pseudo_peripheral_noderpopleftsorteddegreesetrupdateextend)rrstartvisitedqueueparentndchildrens rr r s&q)) ! gG 5'NNE  AHHS6^^g566JqMM J J J%%"%%%x    X rcXt|}d}|} tj||}t||krnW}fd|D}t ||td\}}|S)NrTc3.K|]\}}|k |VdSNr)rrdistls r z)pseudo_peripheral_node..s+>>'!TDAIIAIIII>>rrr) rr shortest_path_lengthmaxvaluesitemsminr#r)rulpvsplfarthestdegr1s @rr r s !A B A<%a++    77  >>>>SYY[[>>>QXXh''Z]];;;3< Hrr/)__doc__ collectionsroperatorrnetworkxr utilsr__all__rrr r rrrrDs%%%%%% #%E F6N6N6N6Nr5J5J5J5Jp"     r